Asymptotic Analysis For The Ruin Probability Of Dependent Risk Models

In insurance risk theory,the measurement of insurance risk is an important issue.The ruin probability is an important index to estimate insurance risk.This paper starts from the insurance risk model,focuses on two types of dependent risk models and estimates related risk quantities.One is the dependent risk model with shot noise process.For this model,we first discuss the Poisson shot noise process.When the shock random variables sequence follow the upper tail asymptotically independence structure or the pairwise negatively quadrant dependence structure,and the shocks have a heavy-tailed distribution,the uniform asymptotics of the tail probability of Poisson shot noise process are derived.On the basis of the above results,we give the asymptotic estimation of the finite-time ruin probability of the dependent risk model with shot noise process.The other is the compound dependent risk model.In this model,we focus on the dependence structure between the inter-arrival times of the accidents and the claim numbers caused by the successive accidents.For the case that the claim sizes follow the upper tail asymptotically independence structure or the pairwise negatively quadrant dependence structure,we investigate the precise large deviations of the aggregate claims in the above risk model.Then,we obtain the asymptotics of the finite-time ruin probability in the compound dependent risk model by using the above results.Moreover,to deal with dependent risk models,this paper first discusses the tail probability property of partial sums of widely orthant dependent random variables.